Hyokyoung (Grace) Hong
Department of Statistics and Probability
Michigan State University

We introduce a quantile-adaptive framework for nonlinear variable screening
with high-dimensional heterogeneous data. This framework has two distinctive features:
(1) it allows the set of active variables to vary across quantiles,
thus making it more flexible to accommodate heterogeneity;
(2) it is model-free in the sense of Zhu, Li, Li, Zhu (2011) as it avoids the difficult
task of specifying the form of a statistical model in a high dimensional space. Our nonlinear
independence screening procedure employs spline approximations to model the marginal effects
at a quantile level of interest. Under appropriate conditions on the quantile
functions without requiring the existence of any moments, the new procedure is
shown to enjoy the sure screening property in ultra-high dimensions.
Furthermore, the quantile-adaptive framework can naturally handle
censored data arising in survival analysis.

We prove that the sure screening property remains valid when the response variable
is subject to random right censoring. Extensive numerical studies demonstrate the fine
performance of the proposed method for various semiparametric models and its
effectiveness to extract quantile-specific information
from heteroscedastic data.